Diagrammatic Monte Carlo method for many-polaron problems.

Area of Science:

• Condensed matter physics
• Quantum many-body theory

Background:

• Polaron problems are crucial for understanding electron-phonon interactions in materials.
• Existing methods often struggle with accuracy at finite electron densities and nonperturbative regimes.

Purpose of the Study:

• To develop a nonperturbative diagrammatic Monte Carlo approach for polaron problems at finite electron densities.
• To accurately describe systems across various regimes, including Fermi liquid and single polaron behavior.

Main Methods:

• Introduced a bold diagrammatic Monte Carlo approach.
• Incorporated high-order vertex corrections for nonperturbative calculations.
• Utilized the Holstein model on a square lattice as a test case.

Main Results:

• Achieved accurate results in the thermodynamic limit for diverse regimes.
• Demonstrated significant accuracy improvements over the self-consistent Born approximation.
• Observed density-dependent changes in quasiparticle effective mass and residue.

Conclusions:

• The novel method provides a robust framework for studying polarons.
• Vertex corrections are essential for accurate nonperturbative polaron descriptions.
• Electron density significantly influences quasiparticle properties in electron-phonon coupled systems.